McGraw-Hill

Forecasting the Si Effect 169
FIGURE S-l
Cumulative Return to Small Size
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1978 1979 1980 1981 1982 1983 1984 1985 1986 1987
MODELING THE SIZE EFFECT
Figure 5-1 graphs cumulative pure returns to size, as measured by
Jacobs and Levy (1988b).' In the following paragraphs, we develop
some models for forecasting these returns. First, however, we discuss
the criteria we used to assess the accuracy of alternative forecasting
methods.
A commonly used measure in portfolio management is the information
coefficient (IC), defined as the correlation between forecast
and actual returns. One drawback of the IC as a forecast evaluation
tool is its independence of both origin and scale. The measured cor
relation between forecast and actual returns is unaffected by adding
a constant to each forecast
multiplying each forecast by a positive
constant. But while IC is invariant to these transformations, the
forecast errors-the difference between forecast and actual retums-clearly
are not. Thus, the IC cannot differentiate between a
perfectly accurate set of forecasts and an alternative set that consistently
overestimates by 50 percent.
The criteria we use assess the accuracy of alternative forecasting
methods more directly than the IC. They are defined in the appendix
at the end of this chapter. The first criterion is mean mor
(ME), which is a simple average of forecast errors. If the ME is pas$